Nuclear Magnetic Moment - Calculating The Magnetic Moment

Calculating The Magnetic Moment

In the shell model, the magnetic moment of a nucleon of total angular momentum j, orbital angular momentum l and spin s, is given by

By projecting with the total angular momentum j we get

has contributions both from the orbital angular momentum and the spin, with different coefficients g(l) and g(s):

by substituting this back to the formula above and rewriting

$= {1\over (j+1)}\left(g^{(l)}{1\over 2} \left(j(j+1) + l(l+1) - s(s+1)\right) + g^{(s)}{1\over 2} \left(j(j+1) - l(l+1) + s(s+1)\right)\right)$

For a single nucleon s =1/2. For we get

and for

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